Self-consistent implementation of nonlocal exchange and correlation in a Gaussian density-functional method

The gradient-expansion approximation (GEA) and the generalized gradient approximation (GGA) to nonlocal exchange energy in concert with the nonlocal correlation energy functional of Perdew [Phys. Rev. B 33, 8822 (1986)] are analyzed when implemented in a fully self-consistent way in conjunction with the Vosko-Wilk-Nusair parametrization for the local exchange-correlation energy. It is shown that the lowest-order gradient expansion, even with corrected asymptotic behavior in the large-density-gradient limit, is still unsatisfactory in the chemically important region of electron densities where the basic assumption of the GEA (‖∇n‖/2${\mathit{k}}_{\mathit{F}}$n${\mathrm{O}}_2$, ${\mathrm{Mg}}_2$, ${\mathrm{CH}}_2$, and for a transition-metal cluster, ${\mathrm{Ni}}_4$.